28 K. LINDERSTR0M-LANG [2 



is a function of X, and an individual one, ai, which is not, we get from 

 Eq. (3) 



'8lnt\ ^_8lnB 

 8X/n 8X 

 for 



(■ 



(4) 



ßi^Bai and 3^=<^iFy 



(5) 



In our attempt to explain the rate curves at 0°C and different pH we have 

 considered the simple reaction 



R — C R— C-O -HOH R— C = 0- -HOH 



: +2H2O ;z::: 



(6) 



Ri— N Ri— ND- -OHa+QH Rj— NH-OHa+QD 



A Ai A2 



where QH is a hydrogen donor or acceptor (H3O, HgO, or OH-) present 

 in constant concentration at constant pH. We have here taken the primitive 

 attitude to assume that the D-atom in the internal hydrogen bond exchanges 

 only by way of the 'hydrolysed' form (Ai), the instabihty of the bond, and 

 therefore the 'availability' of the deuterium atom, being measured by the 

 ratio of the concentrations of forms Ai and A at equilibrium. 

 Using the stationarity principle, we obtain the rate constant 



ß=UQ\i] \\ 



Â:_i , k^[QYl]\ 



ki 



ki j 



(7) 



and if the exchange reaction proper (Aj > A2) is considered the bottle- 

 neck of the over-all reaction, Eq. (7) is transformed into 



ß^keXk^lQU] 



where 



1 



1 



1 + 



^_l l+eàFrl^T 



(8) 

 (9) 



denoting by AFr the free energy of 'hydrolysis' of the hydrogen bond in A. 

 Assuming now that the a-helix is a predominant secondary structure of 

 PDLA in aqueous solution, we may utilize Eq. (9) in the following way: 

 The complete helix of our PDLA contains a maximum of 26 internal hydro- 

 gen bonds with four end-group and three terminal imide hydrogen atoms 

 exposed to water. Adopting the treatment given by Schellman^'-^^-^^ and 

 assuming that the opening of any hydrogen bond along the hehx takes place 

 exclusively through an unwinding of the helix from the ends, we obtain 



1 -y^^-i 



ßi 



l-yl^ 



.y.k.iQU] 



(10) 



